Understanding Tides

• Tides are periodic rises and falls of sea level, caused by Earth's rotation and gravitational forces from the moon and sun.
• Tidal range refers to the height difference between high and low tide.

Understanding Tides

• Equilibrium theory uses idealized world assumptions.
• Dynamic theory considers real-world factors.

Gravitational Forces

• Gravitational force derives from Newton's Law of Universal Gravitation.
• Every object with mass attracts every other object in the universe.
• Gravitational force is proportional to the product of the masses involved.
• Increased mass results in increased force.
• Gravitational force is inversely proportional to the square of the separation distance.
• Gravitational force is greatest at the zenith (point closest to the moon).
• Gravitational force is least at the nadir (point furthest from the moon, opposite the zenith).

Tide-Generating Forces

• Tides are caused by a combination of gravity and motion between Earth, the moon, and the sun.
• The barycenter of the moon and Earth is their common center of mass.
• The barycenter is located beneath Earth's surface.

Inertia: Centripetal Force

• Centripetal force is a center-seeking force.
• Centripetal force maintains planets in orbit via gravitational attraction.
• Centripetal force connects Earth and the moon.

Resultant Forces

• Resultant forces arise from the mathematical difference between gravitational and centripetal forces.

Generating Tides

• No tide generation occurs where resultant forces are vertical relative to Earth's surface.
• Hydrostatic pressure is where resultant forces are parallel to Earth's surface.

Idealized Tidal Bulges

• Water bulges away from and towards the moon.

Tidal Bulges and the Sun's Effect

• Solar bulges are similar to lunar bulges but much smaller.
• The moon is closer to Earth and asserts a greater gravitational force.
• The moon's diameter is 3,478 km (0.27x Earth).
• The Earth's diameter is 12,682 km.
• The sun's diameter is 1,392,000 km (109x Earth).

Phases of the Moon

• New moon refers to the moon being between Earth and the Sun, making it invisible from Earth.
• Waxing crescent refers to the moon moving from the new phase to the first quarter.
• Quarter moon occurs when the moon appears half lit.
• Waxing gibbous refers to the moon moving from its first quarter to its full phase.
• Full moon occurs when the moon and sun are opposite each other.
• Waning gibbous refers to the moon moving from full to last quarter.
• Waning crescent refers to the moon moving from the last quarter to a new moon.

Monthly Tidal Cycle

• Spring tides occur during new or full moons.
• Spring tides have the greatest tidal range and happen during syzygy.
• Neap tides occur during quarter moons.
• Neap tides have the least tidal range and happen during quadrature.

Complicating Factors: Elliptical Orbits

• Perigee is when the moon is closest to Earth.
• Perigee has the greatest tidal range.
• Apogee is when the moon is furthest from Earth.
• Apogee has the least tidal range.
• Proxigean tides occur during spring tide + perigee.
• Proxigean tides are exceptionally high and happen every 1.5 years.

Complicating Factors: Declination

• Declination refers to the angular distance of the Moon or Sun north or south of Earth's equator.
• The sun's max is 23.5 degrees N or S of the equator.
• The moon's max is 28.5 degrees N or S of the equator.
• Overhead of the equator equals equal tides.
• Shifting from the equator equals unequal tides.

Tidal Period

• Tidal period describes the time between high tides.
• From the equilibrium theory, the tidal period is 12 hours and 25 minutes.
• Lunar day refers to time between two successive overhead moons, roughly 24 hours and 50 minutes.
• Solar day refers to time between two successive overhead suns, roughly 24 hours.

Idealized Tide Prediction

• There are two high and two low tides per lunar day.
• There are roughly six lunar hours between high and low tides.

Real Tides: Dynamical Theory

• Continents and friction with the seafloor change tidal bulges.
• Tides are shallow-water waves whose speeds are determined by water depth.
• Idealized tidal bulges cannot form, as unable to keep up with Earth's rotation.

Real Tides

• Crests and troughs rotate around an amphidromic point.
• There is no tidal range at the amphidromic point.
• Cotidal lines refer to simultaneous high tide, with the tide wave rotating once every 12 hours.

Tidal Patterns

• Diurnal tides have one high and one low tide per day.
• Semidiurnal tides have two high and two low tides per day, with tidal ranges about the same.
• Mixed tides have two high and two low tides per day, with the tidal range being variable and most common.

Tides in Coastal Waters

• Bay of Fundy in Nova Scotia has the world's largest tidal range.
• Maelstroms are whirlpools made of rapidly spinning seawater.
• The restricted channel connects two basins with different tidal cycles.
• Tidal bores are tide-generated walls of water that move up certain rivers.
• Conditions for tidal bores include large spring tidal ranges of at least 6 m (20 ft) and low-lying rivers with seaward currents.